Topics Covered

Basics of Density Functional Theory

Density Polarization Functional Theory

Exact-Exchange Density Functional Theory

and Quasiparticle Calculations

Introduction

Density functional theory is an extremely successful approach for the description of ground state properties of metals, semiconductors, and insulators. The success of density functional theory (DFT) not only encompasses standard bulk materials but also complex materials such as proteins and carbon nanotubes.

The main idea of DFT is to describe an interacting system of fermions via its density and not via its many-body wave function. For N electrons in a solid, which obey the Pauli principle and repulse each other via the Coulomb potential, this means that the basic variable of the system depends only on three -- the spatial coordinates x, y, and z -- rather than 3*N degrees of freedom.

An overview over the basic principles of DFT and some neat applications of DFT to real life problems is given in the section ``Basics of Density Functional Theory.'' This section contains a talk that I gave at the Nuclear Physics Seminar at OSU and at the physics colloquium of the University of Braunschweig, Germany. Some application examples are currently studied at OSU (defects in Si and GaN), others (proteins and carbon nanotubes) are taken from the literature.

While DFT in principle gives a good description of ground state properties, practical applications of DFT are based on approximations for the so-called exchange-correlation potential. The exchange-correlation potential describes the effects of the Pauli principle and the Coulomb potential beyond a pure electrostatic interaction of the electrons. Possessing the exact exchange-correlation potential means that we solved the many-body problem exactly, which is clearly not feasible in solids.

A common approximation is the so-called local density approximation (LDA) which locally substitutes the exchange-correlation energy density of an inhomogeneous system by that of an electron gas evaluated at the local density. While many ground state properties (lattice constants, bulk moduli, etc.) are well described in the LDA, the dielectric constant is overestimated by 10-40% in LDA compared to experiment. This overestimation stems from the neglect of a polarization-dependent exchange correlation field in LDA compared to DFT. The section Density Polarization Functional Theory analyzes the properties of this field for real materials.

Rather than approximating exchange and correlation as a functional of the system density, we can also determine the exchange potential exactly. The section Exact-Exchange Density Functional Theory and Quasiparticle Calculations discusses such density functional schemes and their relevance for quasiparticle calculations, that is, computational many-body theory.

To cite this page:
Density Functional Theory
<http://www.physics.ohio-state.edu/~aulbur/dft.html>